No rear Sound from both rear speakers

Could be either, a setting on stereo head unit, fader may have been turned so that sound is just coming from select speakers.
Or could be your front speakers are not wired up or there is a fuse blown.
Note: clicking from turn signal does not come from stereo speakers.

Try another loudspeaker across a rear speaker to check if it is a wiring issue first.
Is the fader control set correctly I wonder.

Assuming the radio has an output for rear speakers and it is connected to them and you have selected the front/rear fader and attempted to adjust it to the rear, you can't do much more without removing the radio and checking the connections and the wiring to the rear speakers.

When I am faced with this problem I disconnect the speaker wiring from the radio and using a 9 volt battery and two lengths of wire I test the speakers and the wiring by connecting to each speaker in turn. A good speaker with good wiring will produce noise when the 9 volt battery is touched to the terminals. If there is no noise the speaker or the wiring is defective.
If all tests ok then the radio is probably faulty. This can further be tested by connecting temporarily to alternative speakers.

x2 the fader or balance set wrong.
bad amp.
or bad speakers.
try a test speaker in place of just 1 speaker, if its dead too. then its the amp.

the amp has 4 , drivers, (4 amp drivers)
any can fail.
even shorted speaker wires or cut.

stock? system.?
or aftermarket
is it hacked?, do you see evidence of hacking at amp or speakers?
did you try adjusting left right , front rear fader knobs yet>
if all looks ok then the head end needs service.
i bench test all radios and amps.
that proves what side is bad.
or while on car, connect a known good speaker to each output that is dead, work now, yes, bad speaker or line.
no, bad head, or fuse in rear of head blown.

I had the exact same sound system in my kia optima & I also had the same problem. The unit has most likely failed as mine did which will require a new unit, you could be very lucky & had the speaker wires fall out or become loose in either case it requires removal of the unit for inspection.

pull the stereo unit out check the rear wires and the rear fuse some times there are 2 fuses 1 for unit its self and another for the amp if its still not working try another cheap radio if that works its the stereo if not there is something wrong with speakers probable worth just replacing head unit will work out cheaper

Both sides or just one?

When speakers go out on both sides at the same time, then usually the issue is with the stereo head unit. If it's wiring is fine, and it's fader setting is set to the front, yet you have no sound, then try this quick test to illuminate a speaker issue possibility:

Using a 1.5 volt battery AA or AAA size is fine. Just briefly connect the battery to the two speaker wires leading to the speaker you wish to test. You need to view the speaker and make sure it is moving in or out. If it operates, then your speaker is working and you can concentrate on your head unit issue.

If both rear speakers failed at the same time then do the following:

1) Check that the fader control on the stereo is set to power the rear speakers.

2) Check continuity of the wires to the rear by disconnecting the head unit (stereo) and testing with a multimeter.

My best guess is that the head unit is either set incorrectly or that it's output to the rear speakers has failed. It's uncommon for both rear speakers to fail at the same time, so the stereo unit is most likely at fault.

Either the balance is off on the head unit, or the the out puts (in the head unit) for the rear speakers are blown.